Standard Form of a Quadratic Equation / Quadratic Function

This video explains how to rewrite quadratic equations and functions in standard form. Here are the key takeaways:

Standard Form:

For quadratic equations: ax² + bx + c = 0
For quadratic functions: y = ax² + bx + c or f(x) = ax² + bx + c
Where a, b, and c are coefficients (numbers), and 'a' cannot be zero.
Key Features of Standard Form:

The term with x² comes first, followed by the term with x, and finally the constant term.
The equation or function is set equal to zero (for equations) or y/f(x) (for functions).
Rewriting in Standard Form: The video demonstrates various techniques to manipulate quadratic expressions into standard form, including:

Expanding parentheses using the box method (or FOIL).
Distributing coefficients.
Combining like terms.
Rearranging terms to have the equation or function set equal to zero or y/f(x).
The video provides three examples to illustrate these techniques, covering cases with parentheses, squared terms, and rearranging equations to equal zero.